Solution to multiple choice questions: cross-tabulations

These are the solutions to the multiple choice questions as given in An Introduction to Medical Statistics, Third Edition. Section references are to the book. 

Solution to multiple choice questions 67 to 73: cross-tabulations

67. TFFFF. Section 13.3. 80% of 4 is greater than 3, so all expected frequencies must exceed 5. The sample size can be as small as 20, if all row and column totals are 10.

68. FTFTF. Section 13.1, Section 13.3. (5-1) * (3-1) = 8 degrees of freedom, 80% * 15 = 12 cells must have expected frequencies greater than 5. It is O.K. for an observed frequency to be zero.

69. TTFTF. Section 13.1, Section 13.9. The two tests are independent. There are (2-1) * (2-1) = 1 d.f. With such large numbers Yates' correction does not make much difference. Without it we get chi-squared = 124.5, with it we get chi-squared = 119.4 (Section 13.5.).

70. TTTTT. Section 13.4-5. The factorials of large numbers can be difficult to calculate.

71. TTTTF. Section 13.7. The more closely related the variables are, the bigger the odds ratio will be. Reversing the order of both rows and columns turns the ad/bc formula to da/cb, the same, but reversing only the columns gives us bc/ad. The ratio of the proportions, or relative risk, would be (a/(a+c))/(b/(b+d)).

72. TTFTT. Chi-squared for trend and Kendall's tau b will both test the null hypothesis of no trend in the table, but an ordinary chi-squared test will not (Section 13.8). The odds ratio (OR) is an estimate of the relative risk for a case-control study (Section 13.7).

73. TTFFF. The test compares proportions in matched samples (Section 13.9). For a relationship, we use the chi-squared test (Section 13.1). PEFR is a continuous variable, we use the paired t method (Section 10.2). For two independent samples we use the chi-squared test (Section 13.1). 

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